Optimizing the Campos-Griffiths-Morris-Sahasrabudhe upper bound on Ramsey numbers

In a recent breakthrough Campos, Griffiths, Morris and Sahasrabudhe obtained the first exponential improvement of the upper bound on the classical Ramsey numbers since 1935. I will outline a reinterpretation of their proof, replacing the underlying book algorithm with a simple inductive statement. In particular, I will present a complete proof of an improved upper bound on the off-diagonal Ramsey numbers and describe the main steps involved in improving their upper bound for the diagonal Ramsey numbers to $R(k,k)\le(3.8)^k$ for sufficiently large $k$.

Based on joint work with Parth Gupta, Ndiame Ndiaye, and Louis Wei.